@afnan_88, you do not need to press the button shifting from R to N to D to 2 so you can flick the gear stick from N to D while revving the engine, not something I would do but that is your choice.
The break is required in City vario to change from P to R. Although as a good practice I keep the break pressed switching from P to R, R to P, R to N, N to R, and N to D.
The gear shifting pages from manuals of Vitz and Honda are posted in some other thread, but I can send you the Cuore shifting page, if you do not have the manual.
I agree with @gem_guy, automatic tranies are designed for comfort and not racing, so save your money and buy a manual tranny driven car, any complications in an auto trany is going to cost you more than an arm and a leg in Pakistan.